Find the product :
(x^3-5x^2+3x + 1)×(x^2-3)
please tell me step by step
Answers
Step-by-step explanation:
(((x3) - 5x2) + 3x) + 1) • (x2 - 3)
x3-5x2+3x+1 is not a perfect cube
Find roots (zeroes) of : F(x) = x3-5x2+3x+1
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
In our case this means that
x3-5x2+3x+1
can be divided with x-1
Polynomial Long Division
Dividing : x3-5x2+3x+1
("Dividend")
By : x-1 ("Divisor")
dividend x3 - 5x2 + 3x + 1
- divisor * x2 x3 - x2
remainder - 4x2 + 3x + 1
- divisor * -4x1 - 4x2 + 4x
remainder - x + 1
- divisor * -x0 - x + 1
remainder 0
Quotient : x2-4x-1 Remainder: 0
difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 3 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Final result :
(x2 - 4x - 1) • (x - 1) • (x2 - 3)
hope it helps you....
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